Abstract

The basic problem in this paper is that of detemnining the geometry of an
arbitrary multiply connected bounded region in R3 together with the mixed boundary conditions,
from the complete knowledge of the eigenvalues {λj}j=1∞ for the negative Laplacian, using the
asymptotic expansion of the spectral function θ(t)=∑j=1∞exp(−tλj) as t→0.

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